In the paper, we explore the behaviour of neural network software qual
ity models, We select a multiple regression quality model from the pri
ncipal components of software complexity metrics collected from a larg
e commercial software system, We train two neural networks; one with t
he complete set of principal components and one with the set of compon
ents selected by multiple regression model selection. Comparisons of t
he three models, for two quality measures gathered from five related s
oftware systems, lead to a better understanding of neural network soft
ware quality models, and the relationship between software complexity
metrics and software quality metrics,